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DETROIT  OBSERVATORY, 

ANN  ARBOR,  MICHIGAN, 

I)ETERMINK1>  BV 
/ 

THE  ZENITH  TELESCOPE 


AND  DISCUSSED  BY  THE 


METHOD  OF  LEAST  SQUARES. 


\ 


4 

( 

LATITUDE 


l‘.Y 

LUDO  VIC  ESTES,  Ph.  D., 

UNIVERSITY  OF  MICHIGAN. 


ANN  AlinOK.  MICH.; 

THE  KEGl.STEK  I'RINTINO  AND  UUBLISHINO  CO. 

1888. 


ERRATA. 


Page  8.  For  AL  read  AA. 

Page  42.  In  third  normal  equation,  for  — 15.580  read  +15.580. 


TABLE  OF  CONTENTS. 


Description  of  Instrument.  .  .  .  .  ^ 

V alue  of  One  Revolution  of  Micrometer-Screw, 

Value  of  One  Division  of  Zenith-Level, 

Star-Places,  ....... 

Observations  for  Latitude,  and  Reductions, 

Discussion  of  Results,  ..... 

Probable  Values  of  R,  D,  (j>,  . 

( 'orrection  of  Computed  Values  of  Latitude, 

Probable  Error  of  Single  Observation, 

Latitude  according  to  Temperature  and  Zenith-Distance, 


PAGK 

1 

8 

11 

12 

19 

40 

48 

49 
58 
54 


rs— 

r 


DESCRIPTION  OF  THE  INSTRUMENT. 


These  observations  were  made  with  a  transit  instrument  con¬ 
structed  by  Fauth  &  Co.,  Washington.  Settings  were  made  by 
a  graduated  circle  on  the  axis,  reading  to  10".  A  zenith-level  is 
attached  to  this  circle.  It  can  be  clamped  to  any  point  on  the 
limb.  The  available  length  of  this  level  is  about  3.5  in.,  or  44 
of  its  own  divisions.  These  are  numbered  each  way  from  the 
middle.  The  tube  has  an  air-chamber  in  one  end.  The  slow- 
motion  screw,  for  moving  the  telescope  on  its  axis,  bears  against 
a  spiral  spring.  In  cold  weather  this  spring  often  failed  to 
respond  promptly  to  a  motion  of  the  screw. 

The  object-glass  has  an  available  diameter  of  3  in.,  and  its 
focal  length  is  3  ft.  10  in.  Its  cell  is  screwed  into  the  tube  of 
the  telescope,  and  it  has  no  adjusting-pins.  Two  eye-pieces 
were  used  :  a  diagonal,  erecting  eye-piece,  magnifying  to  79 
diameters;  and  a  straight,  inverting  eye-piece,  magnifying  to 
67  diameters.  The  latter  was  used  almost  invariably  in  observ¬ 
ing  low  stars,  and  in  a  few  other  cases. 

The  instrument  is  reversed  by  two  arms  which,  by  means  of 
a  lever,  lift  it  out  of  its  wyes.  The  frame  on  which  it  rests 
stands  on  a  brick  pier  rising  about  3.5  ft.  above  the  ground,  and 
extending  two  or  three  feet  below  it.  The  whole  is  inclosed  in 
a  small  wooden  building. 

The  micrometer-box  can  be  revolved  about  the  axis  of  the 
telescope  through  an  angle  of  90°.  It  bears  on  one  side — when 
it  is  in  its  proper  position — against  an  adjustable  pin.  The 
micrometer-wire  is  parallel  to  the  transit-wires.  A  positive 
motion  of  the  screw-head  brings  the  wire  apparently  nearer  the 
screw-head  for  both  eye-pieces,  The  rule  was  always  to  make 
the  last  motion  of  the  screw  positive.  The  whole  number  of 


2 


DESCRIPTION  OF  THE  INSTRUMENT. 


revolutions  of  the  screw  was  read  from  a  notched  scale  in  the 
focus,  its  middle  point  being  numbered  25. 

The  breadth  of  the  field-of-view  is  about  30'.  The  eye-piece 
nan  be  moved  by  a  rack  and  pinion  across  the  field.  The  rela¬ 
tive  positions  of  the  clamp  and  the  screw-head  of  the  microme¬ 
ter  are  thus: 


Direction  of  Star  from  Zenith. 

Position  of  Clamp. 

Position  of  Scriw 

s. 

w. 

Up. 

N. 

w. 

Down. 

S. 

E. 

N. 

E. 

Up. 

The  axis  of  the  instrument  required  adjustment  for  horizon- 
tality  only  once  or  twice  during  the  series  of  observations. 
This  was  secured  by  a  striding-level. 

Errors  of  collimation  and  azimuth  were  kept  within  inappre¬ 
ciable  limits  by  observations  on  a  distant  terrestrial  object. 
However,  during  October  11-21  the  latter  adjustment  was  in 
error  from  the  fact  that  in  making  observation  12,  after  revers¬ 
ing,  the  axis  was  let  down  by  mistake  outside  the  wyes,  so  that 
it  was  afterwards  found  to  have  pushed  one  of  tlie  supporting- 
posts  out  of  place.  Yet,  as  observations  for  azimuth  were  made 
during  this  period  on  stars,  the  observations  for  latitude  were 
retained  and  corrected  for  this  error  of  azimuth,  which  'was 
found  to  be  about  25s. 

High  winds  often  interfered  with  the  accuracy  of  the  obser¬ 
vations,  by  blowing  out  the  lights.  For  this  reason,  notes  of 
the  fact  have  been  made. 

The  centre  of  the  dome  of  the  Detroit  Observatory  is  75.3  ft. 
further  north  than  the  center  of  the  pier  on  which  the  instru¬ 
ment  employed  in  these  observations  rests. 


VALUE  OF  ONE  REVOLUTION  OF  THE  MICROMETER- 

SCREW. 


The  value  which  was  used  in  the  separate  computations  of  the 
latitude  was  determined  by  two  methods:  First,  by  measuiung 
the  difference  of  declination  of  two  known  stars,  this  difference 
not  being  greater  than  the  field  of  view.  The  micrometer-wire 
was  set  on  each  in  succession  without  moving  the  instrument. 
Second,  by  observing  transits  of  stars.  All  the  stars  used  in 
the  first  method  were  taken  from  the  Berliner  Jahrbuch.  The 
symbols  in  the  table  of  reductions  denote  as  follows: 

J<5  =  difference  of  declination  obtained  by  means  of  computed 
apparent  places. 

J-l/  =  difference  of  zenith-distance,  as  measured  by  microm- 
eter. 

JL  =  correction  to  JF  due  to  change  in  the  level  during  the 
observation. 

J/?  =  correction  to  J-k  due  to  differential  refraction. 

Jr  =  correction  to  JT  due  to  hour-angle  of  star.  This  cor- 
rection  is  insensible  to  the  third  decimal  place  in  every  instance 
but  one. 

=  am  -h  AL  +  \p  +  A", 

R  =  Id  /  a:. 

Let  m,  m'  be  the  micrometer  readings  for  the  two  stars, 

“  V  “  inclinations  of  the  level  “  “  “ 

“  7-'  —  r  “  difference  of  refraction  “  “  “ 

“  X,  X  “  reductions  to  meridian  “  “  “ 

all  quantities  being  expressed  in  terms  of  R.  Then, 

(3) 


4 


REVOLUTION  OF  THE  MICROMETER-SCREW. 


micrometer  readings  increasing  upwards, 

^  =  (m' — m)  ±  (Z' — Z)  +  (r' — r)±  —  ir)for  |  ^'  |  stars; 

micrometer  readings  increasing  downwards, 

-(r — C)  =  (m' — m)±{l' — Z) — (/ — r)±{x' — ^c)for  |  |  stars. 


In  the  annexed  table 


d 

u 


placed  after  a  micrometer-reading 


1  1  ,  ,  1  T-  •  (  downwards  ) 

denotes  that  the  readings  increase  |  ^p^r^^ds 

To  each  value  of  R  thus  obtained  was  assigned  the  weight, 
sV  ^  V  X  no.  of  times  observed. 


In  the  second  method  the  determination  rests  principally  on 
transits  of  Polaris.  The  distance  of  the  star  from  the  meridian 


at  each  observation  was  computed  by  the  formula  i 
where 

I  =  observed  interval  in  seconds  of  time, 

d  =  star’s  declination, 

/  sin  15" 

k  =  — - , 

sin  / 

i  =  required  equatorial  interval: 


/  cos  d 
k 


The  values  were  then  combined,  two  and  two,  for  intervals  of 
a  given  number  of  revolutions,  and  the  mean  of  all  divided  by 
the  number  of  revolutions  in  the  given  interval.  The  different 
observations  of  Polaris  were  combined  by  giving  to  each  value 
of  JR,  thus  obtained,  the  weight  sV  rn,  where 

r  =  no.  of  revolutions  in  the  interval  taken, 
n  =  no.  of  such  intervals. 

The  values  of  R  found  from  transits  of  other  stars  were  com¬ 
puted  by  the  formula  i  =  I  cos  <5.  These  values  were  combined 
by  giving  each  star  the  weight  i^ssrn,  where  s  depends  on  the 
declination  of  the  star  and  r  and  n  denote  as  above. 


The  mean  value  of  R  in  each  case  was  then  compared  with 
the  particular  value  from  which  it  was  derived;  and  by  giving 


REVOLUTION  OF  THE  MICROMETER-SCREW. 


5. 


the  squares  of  the  residuals  the  same  weights  that  were  used  in 
finding  the  mean,  the  probable  error,  r%  of  each  of  the  three 
mean  values  of  R  was  determined.  These  values  were  then  com- 

bined  by  giving  to  each  a  weight  proportional  to  - ;  where 

Vr„ 

n  denotes  the  number  of  observations  of  weight  unity  used  in 
determining  one  of  the  values. 


Value  of  One  Reoolution  of  the  MiGTometer-^erew,  Determined  hy  Meamred  Dijferences  of  Zenith-Distance. 


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*  Numbers  in  brackets  ([])  are  doubtful  or  estimated. 
+  Micrometer  reading  changed  7  rev. 

^  Air  unsteady.  §  Air  unsteady.  Windy. 


Value  of  One  Revolution  of  the  Mierometer-Berew,  Determined  hy  Measured  Differences  of  Zenith-Distance. 


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-iJ  C3 


Oi  0) 
CO  72 
Si  Si 
02  02 

PhP4 

t 


.  CO 

72  50 

.CO 
zn  zo 

.  • 

Xfl 

xn 

72  ;o 

a'. 

^  (-H 

<4  <1 

M  CO 

^  • 

d  d 

^pp 

to 

O  Si 

.pp 

LO  4-4 

Q 

CO  '5^ 

CO  ■4*1 

4«*i 

ZD 

'to 

JC 

pp 


Si  Si 

•<1  <i 

CO  Ttl 


02  02 
CO  CO 
Si  Si 
02  02 

P^Ph 

b 


02 


b- 

00 

00 


(M 


ZD 

03 


«o 

03 


Ci 

03 


05 

03 


a 

c3 


05 

02 

pH 


£ 


VALUES  OF  R  TABULATED. 


9 


Values  of  R  Tabulated.  I.  By  Differences  of  Zenith-Distance.  • 


Stars’  Names. 


L  Cass. 
13r.  366 


r 

r  Pegasi  J 

V  Pegasi  I 


K  Pegasi 
16  Pegasi 


35  Arietis 
41  Arietis 


t  Persei 
a  Persei 


<7  Persei 
4  Persei 


Date. 

Temp. 

No.  of  Rev. 

R. 

Means. 

Wt. 

1886,  Dec.  7 

24?9 

36 

// 

45.1660 

8 

28.0 

36 

45.0528 

9 

33.6 

36 

45.0847 

10 

39.0 

36 

45.0191 

1887,  Jan.  5 

14.5 

36 

45.0576 

/ 

4.8 

36 

45.1129 

24 

32.3 

36 

45.0220 

26 

17.8 

36 

44.9617 

29 

37.2 

36 

45.0706 

// 

324 

45.0608 

16 

1886,  Dec.  8 

33.4 

27 

45.1008 

9 

38.6 

27 

45.1112 

1 

54 

45.1060 

3 

9 

42,0 

21 

45.0091 

45.0091 

1 

16 

6.0 

35 

45.0207 

1887,  Jan.  10 

2.3 

35 

44.9657 

24 

31.7 

34 

45.0811 

26 

16.0 

34 

1  45.0157 

29 

36.8 

34 

45.0202 

172 

45.0207 

8 

1887,  Jan.  5 

12.6 

22 

45.1319 

p* 

( 

2.7 

22 

45.0024 

10 

1.3 

22 

45.0056 

66 

45 . 0466 

3 

0 

12.2 

14 

44.9944 

10 

0.8 

14 

45.1286 

Feb.  9 

36.0 

14 

44.9516 

42 

45.0249 

2 

// 


Mean  value  of  R  from  all  pairs  45.0502. 


B 


10 


VALUES  OF  E  TABULATED. 


II.  By  Transits  of  Polaris. 


Date. 

Temp, 

No.  of  Rev. 

No. of  Obs. 

R. 

AVt. 

1886,  Oct.  12  ... . 

8o!5 

10 

14 

// 

45.0185 

1 

19  ... . 

70.0 

6 

15 

45.0088 

U 

22 

20  ... . 

54.7 

10 

44 

45.0000 

Nov.  29 _ 

18.5 

15 

26 

45.0682 

19^ 

1887,  Jan.  3 _ 

3.0 

10 

24 

45.1334 

12 

// 

Mean  value  of  R  by  Polaris  =  45.0477. 


III.  By  Transits  of  Other  Stars. 


Date. 

Temp. 

Wt.  of 
Star. 

No.  of 
Rev. 

No.  of  Obs. 

R. 

AVt. 

1886,  Dec.  4 . 

o 

6.2 

1 

42 

1 

// 

44.7536 

2 

6 . 

22.0 

1 

13 

o 

O 

45.0000 

2 

6 . 

19.7 

1 

40 

1 

44.9700 

0 

7 . 

25.0 

1 

20 

1 

45.2850 

1 

1887,  Jan.  10 . 

1.9 

1 

40 

1 

45.0000 

2 

24 . 

32.5 

1 

20 

2 

44 . 9550 

2 

29 . 

38.4 

1 

20 

2 

44 . 9550 

2 

1886,  Dec.  8 . 

26.8 

1 

20 

2 

45.0150 

2 

9...'.. 

39.6 

2 

15 

5 

45.1098 

8 

9 . 

39.0 

1 

20 

2 

45.0375 

2 

9 . 

38.6 

1 

20 

2 

44.9475 

2 

9 . 

37.5 

2 

15 

3 

44.9230 

4 

1887,  Feb.  24 . 

30.0 

1 

20 

2 

44.9550 

2 

24 . 

25.0 

1 

20 

2 

45.0000 

2 

// 


Mean  value  of  R  =  45,0009. 


Determination  of  R  from  Preceding  Results. 


Method. 

R. 

^0 

No.  of  Obs. 

P 

pR. 

Ad . 

// 

45.0502 

ff 

0.00295 

18.41 

33 

61 

// 

3.0622 

Transits  of  ) 
Polaris...  j 

45.0477 

.00415 

15.51 

65 

101 

4.8177 

Transits  of  .) 
OtherStars  ) 

45.0009 

.01150 

9.33 

35 

33 

0.0297 

195  )  7.9096 

R  =  45.0406 


VALUE  OF  ONE  DIVISION  OF  ZENITH-LEVEL. 


This  was  determined  from  the  number  of  level-divisions 
traversed  by  the  bubble  while  the  telescope  was  turned  on  its 
axis  through  a  definite  angle.  This  angle  was  measured  by 
setting  the  micrometer- wire  on  a  distant  terrestrial  object. 


Mean  value  of  D  =  0.04705. 
r  =  0.001023.  i\  =  0.0002C4. 

Taking  R  =  45 ".0400,  as  previously  found,  D  =  2 ".1192. 


(11) 


STAR  PLACES. 


Of  every  pair  of  stars  used  in  determining  the  latitude  one  or 
both  are  standard  stars.  Most  of  them  are  from  the  Berliner 
Jahrbuch;  and  a  few  are  from  the  American  Nautical  Almanac, 
Connaissance  des  Temps.,  and  Newcomb’s  Standard  Stars. 

The  place  of  every  star  referred  to  B.  A.  C.  was  computed  by 
reference  to  the  catalogues  given  below.  The  weight  of  the 
computed  star-place  was  made  equal  to  the  weight  of  the  cata¬ 
logue  multiplied  by  the  number  of  observations;  except  that  to 
B.  A.  C.  places  a  weight  1  or  0  was  assigned. 

Name  of  Catalogue.  Weight. 

Paramatta,  1835, .  0 

Greenwich  Twelve- Year,  1847, .  4 

Greenwich  Appendix  II.,  1854, . 4 

Greenwich  Appendix  I.,  1862, .  4 

Greenwich  Observations  1861-84, .  4 

B.  A.  C.. .  - 

Washington,  1845-71, . 2 

Second  Kadcliffe,  1860, .  2 

Radcliffe  Observations,  1862-81, .  2 

Glasgow,  Grant, .  1 

Cape,  Stone, .  1 

Second  Armagh . 1 

Harvard  College,  xii., .  2 

Argentine,  1886, . 1 

The  names  of  stars  in  Paramatta  are  not  always  identical 
with  those  given  in  the  other  catalogues. 

The  mean  places  for  the  beginning  of  the  year  were  found  by 
the  formula: 

4'  .=  +  (t  —  n  Cos.  A, 

where  =  the  catalogue  S, 

to  =  the  catalogue  epoch, 
t  =  the  year  for  which  S  is  required. 

A  =  K.  A.  for  epoch 
n  is  taken  from  the  table: 


(12) 


STAR  PLACES. 


13. 


Epoch. 


Log  n. 


1820 

1830 

1840 

1850 

1860 

1870 

1880 

1890 


1.302280 

259 

238 

217 

196 

175 

154 

133 


(Annalen  der  Sternwarte  in  Wien,  Dritter  Folge,  Erster  Band,  1851.) 


Proper  motions  were  computed  by  comparing  the  annual  pre¬ 
cession  with  the  given  annual  variation,  in  the  cases  of  such 
stars  as  were  not  found  in  Auwers’  Fundamental-Catalog,  New¬ 
comb’s  Standard  Stars,  or  other  trustworthy  authorities. 

The  apparent  places  for  the  time  of  observation  were  in  every 
case  computed  by  the  formula 


6  =  fi  g  COS  (6?  +  «')  +  h  cos  (H  +  a')  sin  6'  -f  ^  cos  (i  +  , 


the  star-numbers  being  all  taken  from  the  Berliner  tTahrbuch. 


14 


MEAN  PLACES  OF  STARS  OTHER  THAN  STANDARD. 


Mean  Places  of  Stars  Other  than  Standard. — B.  A.  C.  1657,. 

V  Piscis  Australis. 


Catalogue. 

Epoch. 

Wt. 

N.  P. 

D.,  1886.0 

Paramatta* . 

1825 

0 

B.  A.  C . 

1850 

1 

0 

119 

t 

0 

// 

0.71 

Washington . 

1860 

8 

2.02 

(xreenwicli.  Annendix  I . 

1860 

68 

1.93 

“  Ohserva.tions . 

1861 

32 

1.04 

*  ( 

u 

1862 

4 

3.20 

1863 

12 

2.96 

U 

ii 

1865 

20 

1.36 

ii 

u 

1866 

4 

118 

59 

59.31 

u 

u 

1867 

44 

119 

0 

0.43 

u 

u 

1868 

52 

118 

59 

58.04 

u 

ii 

1869 

28 

58.60 

u 

f 

a 

1870 

1871 

28 

58.61 

u 

ii 

4 

59.04 

u 

a 

1873 

1875 

8 

119 

0 

0.37 

ii 

ii 

4 

118 

59 

58.81 

A  rcrpntine  .... 

1875 

3 

59.85 

TTarvard  Collesfe . 

1875 

34 

119 

0 

0.58 

rirpfinwip.h  Observations . 

1876 

1878 

12 

118 

59 

57.81 

ii 

8 

119 

0 

1.23 

a 

1880 

'  4 

0.49 

B,  ad  el  iff  e . 

1880 

2 

1.43 

On.ne . 

« 

1880 

3 

0.40 

Oreenwie.b  Observations . 

1882 

16 

1.26 

a 

1883 

8 

1.56 

ii 

a 

1884 

4 

2.11 

Proper  motion 

Adopted  mean 

0.00 

place  . 

119 

0 

0.86 

K-  Pise.  Austr.” 


MEAN  PLACES  OF  STARS  OTHER  THAN  STANDARD. 


15 


B.  A.  C.  7930,  20  Piscis  Australis. 


Catalogue. 

1 

Epoch. 

Wt. 

N.  P.  D.,  1886.0 

0  /  // 

Greenwieh  12-5'ear . 

1845 

12 

115  50  11.38 

B.  xV.  C . 

1850 

1 

7.70 

AVashington . 

1860 

4 

’  '  9.11 

Radcliffe . 

1863 

4 

10.66 

(4 

1864 

2 

9.95 

i( 

1865 

2 

9.74 

Argentine . 

1875 

4 

9.17 

Second  xVrmagh . 

1875 

3 

11.97 

Greenwich  Observations . 

1877 

8 

9.86 

1878 

12 

10.05 

Cape . 

1880 

3 

9.73 

Proner  motion . 

0.00 

Adopted  mean  place . 

115  50  10.25 

B.  A.  C.  7987,  Piscis  Australis. 


Paramatta* . 

1825 

0 

123  8  51.4 

Greenwich,  12-year . 

1845 

4 

56.46 

B.  A.  C . 

1850 

0 

50.78 

Greenwich  Appendix  II . 

1850 

16 

50.12 

Washington . 

1860 

4 

53.18 

Argentine . 

1875 

7 

•  53.16 

Cape . 

1880 

3 

54.38 

Radcliffe . 

1880 

2 

56.56 

Greenwich  Observations . 

1883 

8 

58.90 

Proper  motion  taken  from  Cape . 

—  0.09 

Adopted  mean  place . 

123  8  54.06 

*  “  V  Pise.  Austr.” 


16 


MEAN  PLACES  OF  STABS  OTHER  THAN  STANDARD. 


B.  A.  C.  8195,  14  Andromedce. 


Catalogue. 

Epoch. 

Wt. 

K  P.  D.,  1886.0 

B.  A.  C . 

1850 

0 

O  /  // 

51  23  21.58 

Washington . 

1860 

4 

23.49 

Second  Kadcliffe . 

1860 

12 

22.99 

•^Greenwich  Observations . 

1865 

4 

24.33 

1866 

8 

24.26 

Glasgow  . 

1870 

5 

22.92 

.Radcliffe . 

1871 

4 

21.82 

Greenwich  Observations . 

1871 

4 

23.15 

1872 

12 

22.80 

Radcliffe . 

1872 

2 

23.13 

1873 

4 

22.56 

-Greenwich  Observations . 

1873 

16 

23.37 

1874 

16 

23.36 

■  a  a 

1876 

8 

23.16 

66  C( 

1878 

4 

22.65 

66  66 

1879 

8 

24.21 

66  66 

1880 

4 

23.54 

66  6  6 

1881 

4 

22.46 

Annual  proper  motion  computed  from  ) 
Greenwich  Observations . J 

Adopted  mean  place . 

+  0.05 

51  23  23.25 

B.  A.  C.  8348,  Sculptoris. 


B.  A.  C . 

1850 

1 

127  51  44.37 

Argentine . 

1875 

5 

46.89 

Cape . . 

1880 

3 

48.39 

Proper  motion . 

0.00 

Adopted  mean  place . 

127  51  47.11 

MEAN  PLACES  OF  STARS  OTHER  THAN  STANDARD. 


17 


B.  A.  C.  19,  Cassiopeice. 


Catalogue. 

Epoch. 

Wt. 

N.  P.  D.,  1886.0 

O  /  // 

B.  A.  C . 

1850 

1 

38  36  43.30 

Greenwich  Observations . 

1864 

20 

42.91 

Glasgow ..  . 

1870 

3 

44.03. 

Proper  motion . 

0  00 

Adopted  mean  place . 

38  36  43.07 

B.  A.  C.  192,  Sciilptoris. 


Paramatta . 

0 

129.  5  15.10 

B.  A.  C . 

1825 

0 

15.55 

Washington . 

1850 

4 

18.36 

xVrgentine . 

1860 

4 

18.30 

Cape  . 

1875 

3 

18.28 

Proper  motion . 

0.00 

Adopted  mean  place . 

129  5  18.32 

B.  A.  C.  202,  a2  Sculptor  is. 


Paramatta . 

1825 

0 

129  3  0.24 

B.  A.  C . 

1850 

0 

1.62 

Washington . 

1860 

4 

0.33 

Argentine .  •  •  • 

1875 

4 

0.05 

Cape . 

1880 

3 

0.37 

Proper  motion  from  B.  A.  C . 

—0.08 

Adopted  mean  place .  . 

129  3  0.24 

B.  A.  C.  301,  Piscium. 


B.  A.  C . 

1850 

0 

69  8  14.17 

Second  Radclitfe . 

1860 

10 

15.26 

Greenwich  Observations . 

1864 

16 

15.38 

Radclilfe . 

1865 

2 

15.24 

«  .... 

1866 

0 

11.29 

18 


MEAN  PLACES  OF  STABS  OTHER  THAN  STANDARD. 


B.  A.  C.  301,  Piscium. 


Catalogue. 

Epoch. 

Wt. 

P.  D.,  1886.0 

Greenwich  Observations . 

1866 

4 

O  /  // 

69  8  16.49 

RadclifCe . . 

1867 

2 

14.51 

Proper  motion  from  Greenwich  Obs . 

Adopted  mean  place . 

+0.02 

69  8  15.43 

B.  A.  C.  341,  Piscium. 


B.  A.  C . 

1850 

0 

74  56  10.29 

Second  Kadcliffe . 

1860 

6 

3.31 

Greenwich  Appendix  I . 

1860 

32 

3.09 

Glasgow . 

1870 

7 

0.57 

Greenwich  Observations . 

1880 

12 

55  59.42 

U  ii 

V 

1881 

12 

59.73 

Proper  motion  from  Greenwich  Obs . 

+0.17 

Adopted  mean  place . 

74  56  1.60 

B.  A.  C.  492,  X  Andromedoe. 


B.  A.  C . 

1850 

0 

46  11  40.09 

Greenwich  Observations . 

1864 

4 

39.32 

ii  a 

1866 

8 

39.18 

Radclilfe . 

1880 

2 

42.51 

1881 

2 

39.15 

ii 

1881 

6 

39.51 

Proper  motion . 

0.00 

Adopted  mean  place . 

46  11  39.60 

B.  A.  C.  923,  Fornacis. 


B.  A.  C . 

1850 

0 

125  50  4.40 

Cape . 

1880 

3 

0.15 

Proper  motion . 

'  0.00 

Adopted  mean  place . 

125  50  0.15 

OBSERVATIONS  FOR  LATITUDE. 


The  method  pursued  was  as  follows.  Before  the  time  for  the 
appearance  of  the  first  star  the  telescope  was  set  for  the  mean 
zenith-distance  of  the  two 'stars.  The  micrometer-wire  was  set 
where  the  star  would  enter  the  field,  and  the  star  was  bisected 
in  the  middle  of  the  field.  The  readings  of  the  scale,  screw- 
head,  and  level  were  then  recorded.  The  instrument  was  then 
reversed  and  the  process  repeated  for  the  second  star;  the  tele¬ 
scope  having  been  set  by  bringing  the  bubble  of  the  zenith-level 
to  the  middle  of  its  tube. 

In  case  the  bisection  was  made  at  one  side  of  the  middle  of 
the  field,  the  interval  was  either  observed  by  a  chronometer  or 
computed  from  the  estimated  position  of  the  star  in  the  field. 
Values  of  the  latter  kind  are  placed  in  brackets. 

The  values  of  the  latitude  were  computed  by  the  formula: 

) 


(n '  n)  —  (.9 '  -h  s) 

=  A(d'-l-(5)  4=  —  m)R^ - - D  +  \{r  —  r')  -f  {x'  -\-x), 

4 

the  I  I  sigii  being  used  when  the  micrometer-readings  increase 

1 
I 

I  I  =  the  micrometer  reading  for  |  |  star, 

1 


downwards  }  ,  i 
upwards  \  ’ 

I  =  the  declination  of  the  |  |  star, 


=  the  level-readings  for  “  “ 

n,  s  ) 

R  =  value  of  one  revolution  of  the  micrometer-screw,  expressed  in  arc, 
D  —  value  of  one  division  of  the  level,  expressed  in  arc, 
r  —  r'  =  the  difference  of  refraction,  ^ 
x'  ,x  —  the  meridian  corrections. 

For  pairs  north  of  the  equator  r  —  r'  was  taken  equal  to 

dr  dr  « sin  P  * 

^  the  double  sign  denoting  as  above,  and  —  = - . 

dz  dz  cos^  z 


*Cliauv.  Astron.,  ii,  p.  345. 


(19) 


20 


OBSEKVATIONS  FOR  LATITUDE. 


For  stars  below  the  equator  r  —  r'  was  found  from  tables  pre¬ 
pared  for  that  purpose  and  taking  account  of  the  indications  of 
barometer  and  thermometer. 

The  meridian  corrections  were  found  bv  the  formula 

4/ 

iT  -=  [6.1347]  r2  sin  24;  * 

except  in  reducing  the  observations  of  October  11-21,  for  which 
the  formula  used  is 

cos  (j>  cos  4  f  XT  1 

a?  =  i  [6.4357]  - -  for  a  •‘’tar 

sin  2  (  ) 


*Cliauv.  Astron.  ii.,  p.  347. 


Observations  for  LatiUide.  Reductio7is. 


OBSERVATIONS  FOR  LATITUDE. — REDUCTIONS. 


21 


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•22 


OBSERVATIONS  FOR  LATITUDE. — REDUCTIONS. 


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OBSERVATIONS  FOR 


LATITUDE. — REDUCTIONS. 


23; 


49.41 

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**Fnuue  shifted  in  reverging.  See  p.  2.  t  First  observation  poor.  Hazy.  i  Setting  by  zenith-circle,  30°  40’  20"  §Air  unsteady. 

*  Probably  wrong  star  observed. 


Observations  for  Latitude.  liediiotions. 


24 


OBSERVATIONS  FOR  LATITUDE. — REDUCTIONS. 


05 

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Baroiii. 

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Therm. 

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OBSERVATIONS  FOR  LATITUDE.  — REDUCTIONS. 


(Cl 


lC 


C] 

t' 


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•rt" 


REDUCTIONS. 

. 

12 

r— 

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30 

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Hazy.  Moonlight.  t  Very  faint.  J  Con.  cles  Temps  §  Faint,  and  seemed  early.  ** 2  s.  from  edge  of  field.  t+ Atmos,  conditions  good 

iRrobably  wrong  star  observed.  aMicrom.  changed  rev.  sMicrom.  changed  10  rev. 


Observations  for  Latitude.  Reductions. 


26 


OBSERVATIONS  FOR 


LATITUDE  AND  REDUCTIONS. 


03  . 

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OBSERVATIONS  FOR  LATITUDE  AND  REDUCTIONS.  27 


00 

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*  Am.  Naut.  Al.  Both  stars  well  observed.  t  High  wind  $  Newcomb’s  St.  Stars. 


Observations  for  Latitude.  Reductions. 


28 


OBSERVATIONS  FOR 


LATITUDE  AND 


REDUCTIONS. 


m  . 
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Setting  72°  35".  t  Not  well  bisected.  t  Poorly  observed— cloudy.  §  Microni.  changed  to  6.829,  2d  star. 


Observations  for  Latitude.  Reductions. 


30 


OBSERVATIONS 

roll  LATITUDE 

AND  REDUCTIONS. 

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OBSERVATIONS  EOR  LATITUDE  AND  REDUOTIONS 


81 


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t--  r-  t-  t-  i^-  c—  oo  00 


*  Faint.  +  Probably  wrong  star  observed.  See  No.  84.  $  Near  edge  of  field.  §  Microm.  changed  9  rev. 


Observations  for  Latitude.  Reductions. 


32 


OBSERVATIONS  FOR  LATITUDE  AND  REDUCTIONS. 


C/5  . 

S3 

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O 


O) 

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+ 

1 

C 

00 

35 

CO 

(M 

O 

• 

-  35 

(M 

CO 

o 

!>• 

(M 

o 

<3 

O 

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o 


(M 


+ 


G<I 

lO 


+ 


O 

CO 


05 


CO 


(M 

+ 


+ 


CO 

lO 


lO 


(M 


lO 

+ 


CO 

CO 

CO 

lO 

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oi 

00 

lO 

00 

Ol 

OO 

on 

CO 

o 

CO 

CO 

T-H 

o 

(M 

(M 

CO 

(M 

35 

(M 

O 

oo 

CO 

o’ 

CO 

lO 

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c- 

d 

lO 

CO 

CO 

o’ 

CO 

irH 

CO 

(M 

lO 

tH 

»o 

OJ 

o 

o 

00 

00 

t- 

o 

o 

00 

(M 

'cH 

tH 

(M 

lO 

CO 

Tt^ 

CO 

lO 

CO 

lO 

'cH 

CO 

O 

»o 

CO 

t- 

CO 

00 

lO 

CO 

o 

lO 

35 

(M 

rH 

<M 

CO 

T— j 

(M 

CO 

CO 

CO 

03 

rH 

CO 

tH 

i>- 

a  3 

P,<?3 


4- 


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lO 

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o 

»0  00 

• 

tH 

• 

1'- 

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lO 

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(M 

(35 

(M 

O  CO 

CM 

03 

o+j  J-I 
t,<lj  05 

H 


S31 


O 


j-i 

05 


O 
05 
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CM 

CO 

LO 

Ow 

o 

35 

00 

CO 

CM 

O  03 

CM 

1— H 

05 
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CO 

CO 

LO 

LO 

d 

CO 

d 

lO 

CO 

LO 

LO 

lO 

LO  CM 

00 

a' 

I^- 

CO 

O 

r-H 

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t-H 

CO 

CO 

35 

(M 

o  ^ 

t-H 

d 

03 

CM 

+ 

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CO 

d 

CO 

lO 

LO 

lO 

CO 

CO  oo’ 

(M 

3 

CM 

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CM 

00 

r- 

LO 

LO 

35 

o 

C03 

CO 

CO 

■rH 

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oo 

CO 

CO 

to 

•^H 

<50 

CO 

35 

t-  CM 

o 

o 

CO 

o 

.  CO 

35 

CO  tH 

CO 

o’ 

LO 

CO 

00 

o’ 

LO 

00 

CO 

lO 

CO 

CM 

03 

CM 

t-H 

CO 

CM 

CO 

CM 

CM 

CO 

CO 

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<ji 

4^  CU 
CO^Zi 


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c-  r*  • 

92’;?P-i 

gc/2 


<1 

w 


xn 

;-i 

d 

C3 


* 

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tfl 

^  m 
be  xn 
05  <A 

PMO 

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A 

•  S  2 

qSo  2 

•  ^ 

S3 
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r< 


r  a 

(M 

^.<1^ 
^  . 

PPM 


_  •  CO  • 
O  t» 

CC 

J  C3 

O 


w 


00 

CO 


xn  05 
05  (D 

do 
o  ^ 

C<I  CM 


05 

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c« 

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00 

oo 


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00 


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00 


CO 

00 


00 


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00 


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00 


L'” 

00 


00 

00 


OBSEKYATIONS  FOK  LATITUDE  AND  KEDUCTIONS.  88 


'M 

Cl 

X 

O- 

20 

1*^ 

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ir: 

ic 

CT- 

<»«■ 

-r 

CC 

-r 

oc 

1- 

t- 

1'- 

X 

CC 

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IC 

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I.C 

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ct 

C2 

W 

— 

* 

d 

T 

lO 

— 

Ct 

Cl 

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IC 

Cl 

w 

o 

O 

o 

3 

^  ^  . 

^  . 

d 

d 

1 

+ 

1 

I 

+ 

1 

+ 

1— 

X 

Cl 

iC 

O' 

X 

X 

— 

— 

d 

o 

'O 

d 

1 

1 

1 

1 

1 

-F 

1 

1 

1 

•J/z 

-M 

X 

X 

- 

JL 

I.C 

~r 

ic 

Cl 

■M 

-  - 

CC 

I.C 

Cl 

-r 

Cl 

-r 

-Cl 

oi 

Cl 

— 

IC 

Cl 

-J 

+ 

+ 

1 

t 

1 

1 

d 

1 

d 

—  CTi 

CC  '.c 

1 C  Cl 

X  Cl 

CC  1  - 

X 

JC 

“  ::r 

lC  l' 

CC  IC 

—  "S 

CO  X 

w.  CC 

Cl 

1'- 

- 

Cl  Cl 

CC 

-r  cr. 

r-.  CC 

-r  Cl 

L— 

t— 

lO 

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j  c  ^ 

Cl 

T-^  Tt* 

ic 

i-  ro 

t'- 

— -  o 

— •  lO 

L-  I'- 

L— 

X  CC 

1— 

o 

CO 

10! 

i.C  Cl 

H-  iC 

Cl 

CC  -tH 

CC 

CC 

ic 

^  ro 

00 

lO 

C'-  Cl 

X  IC 

O  -f 

Cl  —I 

1—1  CC 

X 

ic 

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CO 

CC  Cl 

Cl  ic 

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r-^  L'* 

CC 

1 

>  d 

c  eo 

00 

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ic 

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Cl 

• 

Cl 

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CC 

Ct- 

Cl 

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Cl 

Cl  C 

>—  X 

l-  ’-C 

Cl  CC 

Cl  — 

Cl 

CO  00 

lO 

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X 

ic  X 

I.C  X 

20 

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CV 

CC 

rc  O 

X  1-H 

IC  o 

O  O' 

Ci 

1'  O'! 

io 

'tT 

to  >0) 

CC  t- 

X  :c 

IC  CC 

i-  ^ 

CC 

— i  ^ 

t'- 

t- 

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t--  'rt' 

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CC 

ic 

00  o 

ol 

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CC  CC 

Cl  — 

CC  I-H 

CC  c; 

1—^ 

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T-H 

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CC  o 

IC 

^  o 

r-H 

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cc 

d 

X  Cl 

1'  CC 

■rr  ic 

X  CC 

d  ^ 

X 

(M  S'! 

<M 

CC 

Cl  Cl 

Cl  Cl 

Cl  Cl 

—  CC 

Cl  CC 

Cl 

CJ 

/ 

, 

..—1 

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<- 

8195 

ndroiii.  1 

^  ^  . 
^  ^  2  x* 

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t-l 

B 

o 

_.  5i' 
c 

'/-  TZ 

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‘T  d 

fafi’S. 

■r.  u 

a  ^ 

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~o 

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c:§  I 

O 

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— 

iX 

ij  2 

Cl  Cl 

CC  CC 

00 

X 

X 

X 

X 

o 

Ci 

C5 

int.  Botli  stars  well  bisected.  t  Probably  wrong  star  observed.  See  obs  70.  ^  Stars  very  steady  S  Microm.  changed  5  rev. 


Observatiovs  for  LnUtnde.  Rediu-Uons. 


34 


OBSEKVATIONS  FOR  LATITUDE 


AND  REDUCTIONS. 


lO 

00 

Cl 

o 

Cl 

GO 

1- 

'00 

t- 

00 

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00 

1C 

1- 

oo 

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Cvl 

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CO 

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d 

o 

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1 

i 

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d 

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CO 

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lO 

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* 

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o 

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T. 

C 

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1 

t  . 

1 

1 

1 

1 

c 

00 

»0) 

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~  t-- 

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<M 

<03 

00 

CO 

w 

o:^ 

1—3 

lO 

d 

o 

d  ' 

+ 

1 

+ 

+ 

+ 

1 

1 

o 

Cl 

00 

o 

o 

00 

CO 

o 

• 

'  V- 

L— 

wi 

CO 

— 

lO 

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lO 

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lO 

lO> 

03 

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uO 

03 

o 

00 

+ 

i 

1 

1 

1 

1 

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CM 

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lO 

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CM 

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lO 

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Cl 

lO 

00 

00 

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1-  00 

cc 

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4-3 

03 

03 

t" 

CO 

CC 

00 

Cl 

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0, 

CO 

lO 

03 

tH 

TP 

03 

c: 

d 

iO 

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<55 

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55 

-rt- 

50 

48 

L'- 

27 

38 

cz 

cc 

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03 

00 

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lO 

w* 

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CO 

o 

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CO 

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00 

1 

03 

i-H 

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lO 

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lO 

CO  ^ 

CO 

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lO 

•  X 

00 

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to 

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o 

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• 

• 

S-  < 

1C 

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X 

CO 

CO  Cl 

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tP 

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H 

03 

Cl. 

d 

1 _ 

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ci 

o 

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O) 

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lO 

r-F 

r-i 

CM 

r— • 

T-4 

Cl  L- 

00 

a;^ 

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03 

d 

d 

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L-- 

lO  CO 

1'-  lO 

1C 

d  d 

> 

<C 

GO 

t- 

<OI 

03 

03 

L—  c:- 

Cl  lO 

iO 

tP  t- 

d 

00 

tP 

W- 

lO 

t-  Cl 

lO  00 

co 

1C 

1C  1C 

s 

1'- 

t-- 

tP 

o 

03 

t'-  I'- 

!C  03 

L- 

03 

tP  Cl 

t— 

tP 

Cl 

03 

iO>  t-- 

CO  oo 

to 

-P 

03  T-H 

c* 

GO 

OO 

<03 

Cl 

lO 

00 

03  (OO 

1C  tP 

00 

t-- 

1C  03 

c 

00 

(03 

tP 

00 

tP 

00 

1— (  'GO 

1C  lO 

— : 

Cl 

CO  »o 

fH 

<03 

(03 

03 

<03 

CO 

03  03 

<Ol  03 

CO 

tH  CO 

, 

J 

, 

Stars’ 

Names. 

doo  £d 

d  i 

.  d 

25 

2 

o 

d  «2‘ 

^  c^ 

C 

<15^ 

CC  C 

CO  . 

.  cn 

O  2 

.  -V 

20 
—  CO 

03 

C  '■'* 

d-5 

c 

.—  ^ 

OO  G 
(M  ” 

5hH 

'=^~0l 

xn 

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Cm 

'TO  (?C 

+t 

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•  -  i-  . 
X  ^  12  ^ 

d  ^ 

e  O 

a5 

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Cl 

w« 

c* 

Cl 

Cl 

Cl 

T*H 

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oo 

GO 

<6 

r-i 

* 

00 

d 

r— ^ 

03 

CO 

o 

Cl 

Cl 

O 

o 

CD 

OBSEUVATIOXS  FOR 


LATITUDE  AND  REDUCTIONS. 


35 


t-- 

0 

»o 

jO 

x> 

03  »0 

00 

00 

rc 

03 

I'-  JO 

re 

30 

00 

rr 

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-f- 

-r 

JO 


lO 

CO 

JO  1' 

03 

03 

0 

0;  03 

0 

30 

CO  CO 

! 

+ 

++ 

i 

1 

1 

lO 

o 


lO 

03 


+ 


03 

+ 


03 

+ 


l'- 

o 

+ 


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t-  1-- 


ir:> 
lO  L-- 

o 


++ 


03 


lO 

lO 


lO 


+ 


30 

»o 

03 


o 

I- 


30 


30 

;o 


»o 

I- 

i-- 


03 

+ 


03 

03 


03 

+ 


-jf 

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JO  03 

x> 

1-* 

30 

L— 

t'- 

30 

0 

03 

00 

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a? 

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03 

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oo 

0 

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1'- 

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t' 

30 

lO  t--  lO 

w» 

1- 

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JO 

CO 

lO 

30 

3  0  -I- 

01 

03 

30 

CO 

1-* 

0 

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30 

30  03  30 

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1— < 

1- 

CO 

CO 

t' 

0 

CO 

30 

03 

03 

03 

CO 

30 

30 

03 

00 

10 

, 

Cl  wJ  CO 

30 

0 

s 

30 

00 

30 

03 

TT 

lO 

CO  CO  03 

30 

CO 

CO 

CO 

CO 

03 

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1 

1 

'  ‘  + 

+ 

1 

+ 

00 

CO 


00  lO 


00 

03 


lO  -• 

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i—  ^ 

d  2 
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03  03-^,- 

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CO 
.  72 

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00 


> 

> 

d 

> 

id 

, 

3^^ 

57 

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l-  30  30 

CO 

l— 

03 

03 

03 

1-H 

L— 

CO 

, 

• 

•  •  « 

• 

• 

• 

• 

• 

• 

• 

• 

» 

• 

c* 

JO 

t'  C-  03 

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1'- 

1' 

JO 

30 

00 

0 

CO 

— 

03 

Cl 

30 

d 

wy 

30 

30 

W^' 

1'- 

CO 

03 

JO 

30 

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t- 

JO 

30 

JO 

t— 

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t-- 

Cl 

30  t-  03 

0 

30 

30 

03 

T— ( 

,3 

CO 

00 

<>1 

30 

Cl  Cl  JO 

03 

Q 

JO 

03 

Cl 

Cl 

00 

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00 

0 

F— 1 

03 

03 

Cl  c:  30 

30 

Cl 

30 

w* 

CO 

t'- 

CO 

30 

a 

.  « 

• 

« 

• 

» 

• 

• 

• 

» 

• 

• 

x> 

03  JO  C 

00 

30 

~r 

30 

03 

cc 

Cl 

JCj 

CO 

03 

03 

—  —  CO 

CC 

f-h 

03 

03 

CO 

03 

03 

03 

03 

03  ^ 

r.  c: 


Hazy  in  nortli.  t  Full  moon.  Hazy  sky.  i  Roth  stars  f^arinf^.  §  Est.  Maf>'.  .'j.O,  i  Est.  Maj;.  r,  3.  Poorly  bisected.  2 Flaring 

3  High  wind.  ^Microin.  changed  5  rev. 


Observations  for  Latitude.  Red/aotions. 


I 


3(5 


OBSERVATIONS  FOR 


LATITUDE  AND 


REDUCTIONS. 


'M 

cc 

CO 

A 

X 

1  . 

-  cc 

CO 

CO 

iC 

• 

. 

*. 

. 

zz  ^ 

rc 

00' 

■00 

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00 

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X 

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^^4 

— +* 

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CO 

w. 

cc 

•  ^ 

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o 

0 

d 

1 

d 

o 

1 

4- 

+ 

d 

+ 

-1- 

1 

, 

OJ 

! 

s-> 

c; 

— 

CC 

1  X 

aj 

d 

d 

■d 

3 

CO 

— 

1 

1 

1 

+ 

+ 

1 

1  o 

• 

00 

lO 

03 

(3 

to 

CC 

* 

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a.' 

'  CO 

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to 

to 

lO 

•— 

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> 

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CO 

d 

d 

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y 

1 

1 

+ 

1 

1 

4- 

1 

1  c 

03 

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CO 

L  — 

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CC 

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— 

CO 

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* 

•• 

— 

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• 

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1 

03 

cc 

03 

■00 

X 

c 

to 

03 

to 

lO 

to 

5 

lO 

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to 

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1 

1 

1 

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r 

j 

+ 

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tr: 

lO  to 

3, 

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L— 

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l'  03 

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lO 

CO 

cc 

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d  -f 

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ac 

— 

1-4 

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0*  to 

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lO 

to 

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tc 

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00 

cc  to 

^  to 

03 

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c- 

O 

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03 

lO 

lO 

03 

03 

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03 

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■O 

00  to 

t— 

03 

CO 

X  to 

C^ 

CO 

1 

1 

t 

to  CO 

03  lO 

lO  CO 

03  to 

CO 

03 

1 

I 

1 

i 

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+ 

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CO 

O 

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, 

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CC  dd 

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o 

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to 

to 

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00 

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CO 

to 

52 

I'- 

X 

O 

— • 

1— ^ 

1— 

OBSERVATIONS  FOR  LATITUDE  AND  Rl^DUCTIONS. 


37 


^  G<i  a 

CO 

L-  CO 

1- 

1- 

JC  o  o 

1* 

CO  o 

50 

03 

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30 

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05 

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-o 

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03 

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o 

o 

o 

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+++ 

o’ 

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o’ 

+ 

o’ 

+ 

T 

— 1  — 

CO 

CO 

CO 

lO 

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o 

o  o 

o 

o 

o’ 

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+ 

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o’  o’ 

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d 

1 

o’ 

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1 

1 

I 

1 

1 

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1—1 

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lO 

t-- 

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CO  CO 

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o 

1- 

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+++ 

o’ 

+ 

o’ 

+ 

n-+ 

>o 

+ 

CO 

1 

1 

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1— 

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&  CO 

CO  CO 

c— 

rc 

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t'* 

t- 

rc 

JO  co’ 

JO 

o'  o 

O  »— 1 

3 

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Cvl 

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o 

o  o  Ol 

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1 

+ 

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1 

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, 

1 

L-  JO 

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1—4 

03 

o 

50  03 

c 

1-  CO  o 

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CO  O' 

CO  o 

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lO 

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CO  o  o 

CO 

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f-H 

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t'-  I'* 

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CO  lO 

r-  lO 

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DISCUSSION  OF  THE  RESULTS  OF  THE  OBSERVA¬ 
TIONS  FOR  LATITUDE. 


The  following  observations  were  rejected,  either  for  failure 
to  fall  within  an  assumed  limit  or  for  reasons  noted  during  the 
making  of  them:  namely,  1,  17,  29,  31,  53,  66,  69,  70,  76,  84,  92, 
96,  second  part  of  107,  113,  127. 

Weights  were  assigned  to  the  observations  on  the  following 
considerations: 

First,  the  atmospheric  and  other  physical  conditions. 

Second,  the  probability  of  the  adopted  star-places.  Where 
both  stars  are  standard  stars  the  weight  140  was  given,  as  also 
where  B.  A.  C.  7657  was  used.  The  weights  of  observations  in 
which  B.  A.  C.  stars  were  used  were,  in  this  respect,  made 
approximately  proportional  to  the  weights  of  the  star-places 
given  in  the  Table  of  Star-Places,  pp.  12-18. 

Third,  the  zenith-distance. 

Fourth,  the  exactness  with  which  the  observation  was  made. 

Fifth,  the  star’s  hour-angle  at  bisection. 

The  adopted  weights  were  then  taken  approximately  propor¬ 
tional  to  the  product  of  the  foregoing  separate  weights,  for  each 
star.  In  observations  like  121,  where  one  star  is  combined  with 
each  of  two  or  more,  the  weight  of  each  result  is  found  by 
dividing  the  weight  of  the  whole  observation  by  the  number  of 
separate  results. 

The  equations  of  condition  were  thus  formed: 

Let  (5,  (V  =  the  declinations  of  the  stars, 

“  R  =  the  true  value  of  one  revolution  of  the  micrometer-screw, 

“  D  =  the  true  value  of  one  division  of  the  zenith-level, 

“  (j)  —  the  true  value  of  the  latitude, 

“  i?o,  Dq,  (po  =  assumed  values  of  the  same  quantities, 

“  i?  =  i^o  +  a;,  D  =  Do -\-y,  ^  =  (p^  +  2, 


(40) 


► 


RESULTS  OF  THE  OBSERVATIONS  FOR  LATITUDE.  41 

Let  !>  =  the  difference  of  refraction, 

“  It  =  the  meridian  correction, 

“  Jf  =  I  (m'  ni),  where  m\  ni  are  the  micrometer-readings, 

“  L  =  ,1  [{n'  +  n)  —  (.s'^  -f  ^vhere  n',  n,  etc.,  are  the  level-read¬ 
ings, 

Then  .]  +  rU)  +  MR  +  LD  +  /;  +  //  —  (/.  =  0. 

I 

Also  by  obs.  1, 

•j  +  ^^^0  +  ADq  -{-  i>  -\-  /j  —  =  0, 

whence  Mx  Ly  —  ^  +  (0i  —  9o)  —  0. 

cTg  was  found  by  taking  the  mean  of  the  results  from  pairs  of 

standard  stars  of  zenith-distance  less  than  30°,  and  difference 

« 

of  zenith-distance  less  than  11^;  the  level-correction  being  less 
than 

=  42°  16'  47.87^^ 

The  observations  were  divided  into  five  sets,  according  to  tem- 
Xierature,  and  as  many  sets  of  normal  equations  were  formed. 

In  order  to  reduce  :!/,  '^x  was  substituted  for  x  in  the  equation 
of  condition,  where  v  =  10. 


4 


42 


DISCUSSION  OF  RESULTS. 


Temperature  6()°-7o°. 


No. 

M 

L 

n 

l/  wt. 

Equations  Weighted. 

5 

—8.84 

—1.27 

+0.26 

1.0 

—  0.88  vx  —  1 .27  2/  —  ^  +  0.26  =  0 

6 

—14.27 

—0.17 

—1.42 

.9 

—  1.28  r-oj  —0.15  2/  —0.90.?  —  1.28  =  0 

7 

+7.52 

+2.35 

+0.02 

.9 

+  0.68  vx  +  2.11  y  —  0.90  ?  +  0.02  =  0 

8 

—8.89 

—0.30 

+0.31 

1.0 

—  0.89  vx  —  0.30  ?/  —  ?  +  0.31  =  0 

9 

—10.01 

-1.17 

+0.61 

1.0 

—  1.00  vx  —  1.17  y  —  .?+ 0.61=0 

10 

+13.63 

—0.32 

+0.06 

.7 

+  O.dovx  —0.22  y  —0.70?  +  0.04  =  0 

11 

—1.08 

—0.15 

—1.27 

.6 

—  0.06  vx  —  0.09  y  —  0.60  ?  —  0.76  =  0 

12 

—1.03 

—0.02 

+  1.01 

.6 

—  0.06  vx  —  0.01  y  —  0.60  ?  +  0.61  =  0 

13 

—10.12 

—0.05 

—1.54 

1.0 

—  1.01  vx  —  0.05  ?/  —  z  —  1.54  =  0 

14 

—3.81 

0.00 

+  1.54 

1.0 

—  0.38  vx  +  0.00  y  —  ?  +  1 .54  =  0 

15 

+0.39 

+0.05 

—1.58 

.4 

+  0.02  vx  +  0.02  y  —  0.40  ?  —  0.63  =  0 

16 

—10.18 

+  1.60 

-0.55 

.6 

—  0.61  v2'  -f-  0 . 96  —  0.60?  —  0.33  =  0 

18 

—10.68 

-0.52 

-0.01 

.4 

—  0.43  vx  —  0.21  y  —  0.40  ?  —  0.00  =  0 

19 

+0.54 

—2.32 

+  0.54 

.8 

+  0 . 04  I’a?  —  1 . 86  2/  —  0.80  ?  +0.43  =  0 

20 

—8.92 

-0.20 

—0.85 

.9 

—  0.80i'a?  —0.18?/  —0.90?  —  0.76-.=  0 

21 

+13.60 

—0.17 

—0.15 

.9 

^  1.22  vx  —0.15  y  —0.90?  —  0.13  =  0 

22 

—3.84 

—0.30 

—0.03 

.9 

—  0.35  vx  —  0.27  y  —  0.90  ?  —  0.03  =  0 

23 

—8.95 

—0.07 

—1.40 

1.0 

—  0.89  vx  —  0.07  2/  —  ?  —  1;40  =  0 

24 

—10.09 

—0.17 

-0.05 

1.0 

—  1.01  ra?  —  0.17  2/  —  ?— 0.05  =  0 

25 

+  13.62 

—0.15 

+  1.10 

1.0 

+  1.36  w —0.15  ?/  —  ?+ 1.10  =  0 

26 

—3.89 

—0.07 

— 1 . 16 

1.0 

—  0.39  vx  —  0.07  2/  —  ?  —  1 . 16  =  0 

NORMAL  EQUATIONS. 

+  13.363  +  3.571  2/  +  5.472  ^  +5.462  = 
+  ‘S.7>Hvx  +12.218  2/  +  3.228  2  —1.717  = 
+  5.472  rx'  3.228  2/  —15. 580  z  +2.460  = 

SOLUTION. 

rx  +  [0.42688]  y  +  [9.61224]  ^  +  [9.61168]  = 
2/  +  [9.19529]  2  +  [9.45045]  = 
^  +  [8.kl32]  = 

The  niiinbers  in  brackets  are  logarithms. 


0, 

0, 

0.. 


0. 

0, 

0. 


Value. 

Weight. 

Probable  Error. 

/  / 

X  =  —  0.0464 

1093 

/  t 

0.0157 

2/  =  +  0.2908 

11 

0.1551 

?  =  —  0.0551 

13 

0.1426 

m  =  21,  n  = 

3,  {}in  ■  3]  =  10.502, 

/[nn  -3] 

'  =  0.6745  u'  >M  —  ii  =  0.5152. 


I 


DISCUSSION  OF  RESULTS. 


43 


Temperature  45° -ao^. 


Xo. 

U 

L 

n 

1  wt. 

Equations  AVeighted. 

Q 

W 

+7.60 

+1 . 52 

+1.78 

0.9 

+  0.68  VX  +  1.37  ?/  —  0.90  +  1.60  =  0 

•  > 

o 

5.48 

—0.22 

—0.54 

.9 

—  0.49  vx  —  0.20?/  —  0.90.?  — •  0 . 49  =  0 

4 

—2.98 

—1.27 

+0.88 

.7 

—  0.21  vx  —0.89?/  —0.70?  +0.62  =  0 

4 

—9.06 

—0.20 

—0,56 

.  7 

-  0.63  vx  —  0.14  y  0.70  ?  -  0.39  =  0 

27 

+7.60 

—0.05, +0-.33 

.6 

+  0.46  va;  —  0.03  ^  0.60?  +0.20  =  0 

28 

— 16.54 

0.00 

—1.67 

1.0 

1 . 64  J'o;  +  0 . 00  ?/  ?  —  1 . 67  :=  0 

30 

18.48 

+0.47+1.34 

.9 

1.66  vx  +  0.40  y  0.90?  +  1.21  =  0 

32 

—8.96 

+0.42 

-0.67 

1.0 

—  0.90  +  0.42  ?/  ?  0.67  =  0 

o*> 

OO 

—10.10 

+0.02 

+0.16 

1.0 

—  1 . 01  va?  +  0 . 02  ?/  -  ?  +  0 . 16  =  0 

34 

+13.58 

—0.50 

— 1 . 26 

1.0 

+  1.36  vx  -  -  0.50  y  ~  ?  —  1.26  =  0 

35 

—3.87 

-0.15 

—0.26 

1.0 

—  0.39  i'a;  0.15?/  —  ?  —0.26  =  0 

36 

+7.61 

—0.22 

+0.78 

.9 

+  0.68  vx  -  0.20  y  —  0.90  ?  +  0.70  =  0 

37 

-  5.63 

+2.30 

+0.25 

.9 

—  0.51  vx  +  2.07  y  0.90?  +  0.22  =  0 

38 

*10.85 

+1.87 

—1.24 

.4 

-  0.43  vx  +  0.75  y  0.40  ?  -  0.50  =  0 

39 

—8.93 

-0.17 

—0.44 

1.0 

0 . 89  I'X  —  0.17?/  —  ?  —  0 . 44  =  0 

40 

—10.11 

+0.12 

—0.16 

1.0 

- 1 . 01  ?  +  0 . 12  ?/  —  ?  —  0 . 16  =  0 

41 

+13.62 

-0.05, +1.49 

1.0 

+  1.36  v.t; —0.05?/  -  -  ?  +  1.49  =  0 

42 

—3.88 

0.00 

—0.12 

1.0 

0.39  +  0.00  ?/  ?  -  0.12  =  0 

43 

+7.56 

+0.17 

-0.10 

.9 

+  0.68  +  0.15  ?/  0.90?  -0.09  =  0 

44 

—5.56 

+0.07 

0.11 

.9 

-  0 . 50  vx  +  0 . 06  ?/  -  0 . 90  ?  0 . 10  =  0 

45 

—10.84 

+1.67 

-0.38 

.4 

-0.43  vx  +  0.67  y  -  0.40?  -0.15  -  0 

46 

+6.96 

—0.15 

+0.92 

1.0 

+  0.70  —  0.15  ?/  ■  ?+ 0.92  =  0 

47 

+8.76 

—0.17 

—1.29 

.9 

+  0.79  w  —1.53?/  —0.90?  —1.16  =  0 

48 

+7.57 

—0.37 

—0.51 

.9 

+  0.68  )’a?  —0.33?/  0.90?  -0.46  -=0 

49 

— 5.52 

+0.05 

+1.61 

.9 

— ^0.50  vx  +0.04?/  0 . 90  ?  +  1 . 45  =  0 

50 

—12.08 

+0.22 

+0.93 

.6 

0.72  vx  +  0.13  y  0.60  ?  +  0.56  =  0 

NORMAL  EQUATIONS. 

+  18.596  i-jc  -  3.813?/+  4.033  z  +  2.610  =  0, 
3.813  +  11.238  ?/  1 .094  z  +  4.382  =  0, 

+  4.033  i’.r  1.094  ?/ +  20.120  z^  0.939  =  0. 

SOLUTION. 


+  [0 . 31885  n]  ?/  +  [9 . 33621]  z  +  [9 . 15218]  =  0, 

y  +  [8 . 40714  nj  z  +  [9 . 67286]  =  0, 

.  z  +  [8.85759  w]  =  0. 


Value. 

AV  eight. 

Probable  Error. 

// 

// 

a;  =  0.0254 

1663 

0.0134 

y=  0.4689 

10 

0.1689 

r  =  +  0.0720 

19 

0.1245 

m  =  26,  /?  =  3,  \nn  •  3]  =  15.069, 

// 

r  =  0.5459. 


4 

51 

52 

54 

55 

56 

57 

5S 

59 

()0 

61 

62 

66 

()4 

65 

67 

(iS 

71 

71 

72 

88 

89 

90 

91 

i)7 

98 

‘)9 


DISCUSSION  OP  EESULTS. 


Temperature  30° -45°. 


M 


L 

n 

wt. 

60 

— 0 . 55 

—0.40 

1.00 

66 

—1.95 

+0.38 

.90 

80 

-0.10 

—1.84 

.40 

13 

+0.22 

—0.88 

.90 

92 

—0.10 

--0..  19 

1.00 

13 

+0.37 

—0.35 

1.00 

56 

0.00 

—0.66 

.70 

90+0.15 

—0.49 

1.00 

56 

—0.22 

—0.39 

.90 

77 

—0.32 

—0.63 

.40 

12 

+0.02 

—0.39 

.60 

04 

—0.40 

+0.94 

.70 

55 

+0.10 

+0.15 

.90 

22 

+0.50 

— 0.57 

1.00 

34 

0.00 

—0.50 

.20 

17 

_  0.00 

—2.30 

.08 

88 

—0.22 

—0.34 

.20 

37 

+0.15 

—0.58 

.20 

89 

—0.45 

—1.57 

1.00 

59 

—0.05 

+1.14 

.90 

53 

1—0.47 

+0.59 

.90 

69 

1—0.55 

—0.35 

.50 

'  I 

15 

+0.22 

—0.35 

.08 

.67 

i  0.05 

1 

—0.43 

.50  1 

.01+2.72 

+0.08 

.08. ! 

.35 

:-0.47 

+0.94 

.90 

.88+0.10 

.30 

i 

Equations  Weighted. 


+  1 . 36  vx  —  0 . 55  y 
-f-  0.69  —  1.75  y 

—  0.43  vx  —  0.04  y 

—  1.09  vx  +  0.20  .V 

—  0.89  vx  —O.Wy 

—  1.01  vx  +0.37  y 
+  0 . 95  vx  +  0 . 00  y 

—  0.39  vx  +  0.15  y 
— •  0.50  vx  —  0.20  y 

—  0 . 43'  vx  —  0 . 13  y 

—  0.73  vx  +  0.01  y 
+  0.49  vx  —  0.28  y 
+  0.68  i’.r  +  0.09  ?/ 

—  0.92  vx  +  0 . 50  y 
0 . 25  vx  +  0 . 00  y 

+  0.02  vx  +0.00?/ 
+  0.14  vx  0.04?/ 
.-  0.05  vx  +0.03?/ 
0 . 39  vx  -  0.45?/ 

+  0.68  vx  0.04  y 
0.50  vx  ,  0.42^' 
+  0.18  vx  0.27  y 
+  0.03  ?'.?:  0.02  y 

+  0.18  vx  —  0.02  y 
+  0.02  vx  +  0.22  y 
-  0.21  vx  0.42  y 
0.24  vx  +  0.03  ?/ 


2  —  0.40  =  0 

—  0.90  ^  +  0.34  =  0 

—  0.40  2  —  0.74  0 

—  0.90  '  —  0.79  =  0 

_  2  _  0.19  =  0 

—  2—0.35  =  0 

—  0.70  2  —  0.46  =  0 

—  2  —  0.49  =  0 

—  0.90  z  0.35  =  0 

—  0.40  2  —  0.25  =  0 

% 

—  0.60  2  —0.23  =  0 
0.70  2  +  0.66  =  0 
0.90  2  +  0.13  =  0 

2  —  0 . 57  =  0 
0.20  2  -  0.10  =  0 
0.08  2  —  0.18  -=  0 

—  0.20  2  0.07  =  0 

0.20  2  —  0.12  =  0 

2  1.57  =  0 

0.90  2  +  1.03  =  0 

—  0.90  2  +  0.53  =  0 
0.50  2  —  0.17  =  0 

—  0.08  2  -  0.03  =  0 

0.50  2  —  0.21  =  0 
0.08  2  +  0.01  =  0 
0.90  2  +  0 . 85  =  0 
0.30  2  0.63  =  0 


1 


DISCUSSION  OF  RESULTS.  45 


'Ttmpe rattire  3()°-45°.  Concluded. 


Xo. 

51 

L 

n 

C  wt. 

Equations  Weighted. 

101 

--3.81 

+2.00 

+1.11 

.20 

—  0.08 /’o;  +  0.40  2/  0.202+0.22  =  0 

102 

-^0.58 

+0.40 

—1.05 

.90  ; 

j 

—  0.05  vx  +  0.36  y  -  0.90  z  0.94  =  0 

103 

— 5 . 56 

-0.17 

+0.12 

.60  1 

—  0.33rx  0.10?/  —0.60  2  +  0.07  =  0 

104 

—10.80 

-0.05 

+0.53 

.30  i 

-  0.32  j-.r  0.017/  0.30  2  +  0.16  =  0 

105 

+3.63 

+1.40 

+0.73 

.50  i 

+  0.18  rx  +  0.70  y  -  0.50  ^  +  0.36  =  0 

106 

+2.54 

+0 . 35 

—1.00 

.20  ’ 

+  0 . 05  I'a:  +  0 . 07  ?/  0 . 20  2  0 . 20  =  0 

107 

+8.78 

-3.37 

—0.61 

.05  ! 

+  0.04  vx  -  0.17  ?/  0.05  2  —  0.03  =  0 

108 

—7.81 

—1.22 

—0.42 

.30 

-  0.2^  vx  0.37?/  0.30  2  0.13  =  0 

109 

—0.57 

+0.67 

—0.02 

.90  ^ 

—  0.05  vx  -[■  0.60  ?/  0.90  2  0.02  =  0 

V2\) 

-0.56 

+0.07 

—0.18 

1.00  i 

1 

— ^0.06  vx  +  0.07  ?/  —  2  '  0.18  =  0 

130 

+15.08 

-0.05 

+0.43 

.40  1 

+  0.60  vx  —  0.02  y  ^  0.40  2  +  0.17  =  0 

131 

+1.03 

-0.20 

-0.19 

.30 

+  0.03  vx  -  0.06  y  —  0.30  2  -  0.06  =  0 

131 

+1.12 

—0.20 

—0.22 

.20  1 

+  0.02r.r  0.04?/  0.20  2  0.04  =  0 

131 

+3.03 

—0.20 

-0.63 

.20 

+  0.06  vx  0.04  y  0.20  2  -  0.13  =  0 

135 

—7.01 

+0.12 

—0.32 

1.00 

—  0.70  vx  +  0.12  ?7  2  —  0.32  =  0 

136 

+1.04 

—0.30 

+0.49 

.40 

+  0.04va;  -  O.V2y  0.40  2  +  0.20  =  0 

136 

+1.19 

-1.42 

+0.50 

.30 

+  0.04  -  0.43?/  0.30  2  +  0.15  =  0 

136 

+3 . 0/ 

—0.77 

+0.39 

.30 

+  0.09  vx  -  0.23  y  —  0.30  2  +  0.12  =  0 

137 

+1.10' +0.15 

+0.16 

1.00 

+  0.11  +  0.15  V  2+0.16  =  0 

138 

+7.28 

—0.15 

—1.05 

.90 

+  0.66  vx  0.13  y  -  0.90  2  —  0.94  =  0 

NORMAL  EQUATIONS. 

+  11.829  vx  —  2.556  y  +  2.260  2  +  3.290  =  0, 

—  2.556  vx  +  6.290  2;  +  1.685  s  —  0.920  =  0. 

+  2.260  vx  +  1.685  2/  +  21.032  0  +  4.490  =  0. 

SOLUTION. 

r:r  +  [9 . 33462^2]  2/  +  [9 . 28117]  ^  -]-  [9 . 44426]  =  0, 
y  +  [9.57830]  5:  +  [8.56139n]  =  0, 


2  +  [9.29934]  =  0. 

Value. 

Weight. 

Probable  Error. 

/  t 

x  =  —  0.0216 

1037 

!  1 

0.0093 

?/  =  +  0.1119 

6 

0.1281 

z  =  _  0.1992 

20 

0 . 067 6 

7n  =  47,  y  =  3,  [nn  •  3]  =  8.749,  y  =:  0..3008. 


c 


46 


DISCUSSION  OF  RESULTS. 


Temperature 


Xo. 

U 

L 

n 

wt. 

• 

Equations  Weighted. 

75 

+7.57 

—0.10 

+0.34 

0 

90 

1 

+  0.68 

vx 

—  0.09  ^ 

0. 

90  2 

+  0 

77 

+2.52 

+0.75 

+0.90 

20 

!  +0.05 

vx 

+  0.15  y 

0 

20  ^ 

+  0 

78 

-9.17 

—0.75 

-0.23 

1 

00 

i  —0.92 

vx 

—  0.75  V  - 

- 

z 

0 

79 

+3.66 

+0.45 

+0.13 

50 

i  +0.18 

vx 

+  0.22  V  - 

0. 

50  ^ 

+  0 

80 

+2.26+0.65 

+1.20 

30 

1  +  0.07 

vx 

+  0.19  y  - 

-  0 

30  2 

+  0 

81 

--0. 52 +0.47 

+1.55 

1 

00 

-  0 . 05 

vx 

+  0.47  V  - 

- 

+  1 

82 

+2.  a) 

-1.62 

+0.01 

20 

+  0.05 

vx 

—  0.32  y  - 

-  0 

20  2 

+  0 

83 

+2 . 49  j +0 . 25 

-  1.53 

.20 

+  0.05 

vx 

+  0.05  y  - 

-  0 

20  2 

—  0 

85 

+3.69 

—0.30 

-  0.17 

.50 

+  0.18 

vx 

--  0 . 15  y  - 

-  0 

50  2 

--  0 

86 

+2.26 

+0.02 

-  0.24 

.30 

+  0.07 

vx 

+  0.01  y  - 

-  0 

30  2 

--  0 

87 

-7.91 

+0.50 

—1.60 

.40 

—  0.32 

vx 

+  0.20;v  - 

-  0 

40  2 

-  0 

93 

—7.86 

-0.05 

- -0.58 

.40 

0.31 

vx 

—  0 . 02  i/ 

0 

40  2 

-  0 

94 

0.54 

+0 . 05 

-0.39 

1 

.00 

-  0.54 

vx 

+  0.05  y  - 

- 

X 

-  0 

95 

+7.59 

-0.15 

+0.62 

.80 

+  0.61 

vx 

-  0.12  y  - 

-0 

80  2 

+  0 

116 

+2.50 

-1.65 

-  0.14 

.70 

+  0.17 

vx 

--1.15?/ 

-  0 

70  2 

0 

117 

+2.62 

-  -0.45+0.52 

.30 

‘  +  0.08 

vx 

—  0.13  y  - 

-  0 

.30  2 

+  0 

118 

2.40+0.72 

+0.71 

.70 

1  -0.17 

vx 

+  0 . 50  1/  - 

0 

.70  2 

+  0 

119 

+7.10 

-0.07 1+0. 83 

.06 

j  +0.04 

vx 

--  0.00  y 

-  0 

.06  2 

+  0 

oi 

oi 


0 

0 

0 

0 

0 

0 


0 


NORMAL  EOI^ATIONS. 

+  2.321  vx  +  0.177  y  +  0.384  2  +  1.000  =  0, 

0.177  L-c  +  2.673  y  +  0.758  2  +  1.119  =  0, 

+  0.384  vx  +  0.758  2/  +  6.644  2  —  1.643  =  0. 

SOLUTION. 

vx  +  [8 . 88229]  y  +  [9 . 21865]  2  +  [9 . 65963]  =  0, 
2/  +  [9 . 43785]  2  +  [9 . 59132]  0, 

2  +  [9 .51774/i]  =  0. 


Yalue. 

Weight 

Probable  Error. 

// 

// 

X  =  -  0.0475 

191 

0.0195 

y  =  —  0 . 4805 

0 

0 

0.1679 

2  -  0.3294 

() 

0.1067 

// 

m  =  18,  y  =  3,  [nn  ■  3]  =  2.396,  r  =  0.2696. 


/ 


» 


DISCUSSION  OF  RESULTS. 


47 


Temperature  o°-15°. 


Xo. 

L 

11 

y  wt. 

! 

1 

/  0 

12.30 

1.52 

—1.24 

0.30 

+3 , 80 

2.50 

—0.93 

.50 

no 

10.80 

—0.80 

—1.01 

.30 

111 

+3.72 

—0.65+0.52 

.50| 

112 

+3.16 

—0.50+0.38 

.08 

114 

-0 . 50 

—0.87 '+0.52 

.90 

115 

2.53 

+3.07+0.20 

1.00 

120 

—0.52 

-0.02 

+2.08 

1.00 

121 

+1.00 

+1.25 

—0.06 

.30 

121 

+1.08 

+1.25 

+0.15 

.20 

121 

+2.96 

4-1.65 

—0.88 

.20 

122 

+2.63 

+0.05 

+1.76 

.20 

123 

— 2.9,7 

+0.05 

+0.89 

.60 

124 

+1.12 

+0.65 

4-0 . 50 

.30 

124 

+3.03 

+0.62^+0.06 

.30 

125 

—2.46 

+2.471+1.60 

.40 

126 

--3.88 

+1.45 

—2.20 

.10 

128 

-  -2.46 

+1.95 

-0.37 

.90 

132 

+6.01 

—0.65 

+1 . 85 

.04 

133 

+15.10 

-0.55 

+0.39 

.40 

134 

+1.04+0.42 

+1.99 

.40 

134 

+  1.12'4-0.42 

+1.26 

.30 

134 

+2.97  +1.55 

+0.51 

.30 

i 

I 

Equations  Weighted, 


0.37  rx 
-f-  0 . 10  vx 

—  0.32  vx 
+  0.19  vx 

0 . 03  vx 

-  0.04  vx 

—  0.25  vx 

—  0.05  vx 
+  0 . 03  vx 
4-  0 . 02  vx 
-j-  0 . 06  vx. 
4-0.05  vx 

—  0 . 14  v.r 
+  0.03  vx 
+  0.09  vx 

-  0 . 10  vx 
— -0.04  vx 

—  0.22  vx 
0. 02  vx 

+  0.60  vx 
+  0 . 04  vx 
+  0 . 03  vx 
4-0.09  vx 


-  0.46  y 
--  1.2b  y 

—  0.24  y 

—  0.32  y 

-  0.04  y 

—  0.78  V 
+  3.07  y 

—  0.02  y 
+  0.37  y 
4-  0 . 25  2/ 
+  0.33  y 
+  0.01  y 
+  0.03y 
+  0.19  y 
4-  0.19  y 
+  0.99  y 
+  0.14  y 
+  1-75  y 

—  0 . 03  i/ 
--  0.22  y 
+  0.17y 
+  0.13  V 
+  0.46  y 


^  0.30  z 
-0.50  2 

—  0.30  2 

—  0.50  2 
-  0.08  2 

--0.90  2 
2 

-  2 

—  0.30  2 

—  -  0.20  2 
—  0.20  2 
-  0.20  2 
-  0.60  2 

—  0.30  2 

—  0.30  2 
-0.40  2 

—  0.10  2 
-0.90  2 
-  0.04  2 

—  0.40  2 

-  0.40  2 
-0.30  2 

0.30  2 


-  0.37  = 

-  -  0.46  = 

0..30  = 
+  0.26  = 
+  0.03  = 
+  0.47  = 
+  0.26  = 
+  2.08  = 

—  0.02  = 
+  0.03  = 
—  0.18 
+  0.35  = 
+  0.53  - 
+  0.15  = 
+  0.02  = 
+  0.64  = 
—  0.22  = 
--  0.33  = 
+  0.07  = 
+  0.16  = 
+  0.80  = 
+  0.38  = 
-f  0.15  = 


0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 


NORMAL  K(^UATIONS. 

+^0.846  vx  —  1.303  y  +  0.313  2  +  0.118  =  0, 

—4.303  vx  +  16.720  y  —  3.852  2  +  1.358  0, 

0.313  vx  -  3.852  y  +  5.728  2  —  3.350  =  0. 

SOLUTION. 


vx  +  [0 . 18757n]  t/  +  [9 . 56817]  2  +  [9 . 14451]  =  0, 
2/  +  [9 . 35993n]  2  +  [9 . 01982]  =  0, 
2  +  [9.79817n]  =  0. 


Value. 

Weight. 

Probable  Error. 

/  / 

X  =3  —0.0311 

74 

t  / 

0.0387 

7/  =  +  0.0392 

13 

0.0937 

2  =  +  0.6283 

5 

0.1517 

m  =  23,  y  =  3,  [nn  •  3]  ^4.898,  r  =  0.3338, 


48 


DISCUSSION  OF  RESULTS. 


As  the  results  of  the  foregoing  five  sets  of  equations  indicate 
no  temperature-corrections  to  the  values  of  E  and  D,  the  fol¬ 
lowing  set  of  equations  was  formed  from  all  the  observations. 

NORMAL  EQUATIONS  FORMED  FROM  ALL  THE  OBSERVATIONS. 

-h  46 . 955  vx  —  3 . 924  y  +  12 . 462  ^  +  12.573  =  0, 

—  3.924  +  49.139  y  +  0.725  4.225  =  0, 

+  12.462  1W+  0.725  ?/  +  69.104  ^  +  1.018  =  0. 

SOLUTION. 

rx  +  [8.92205a]  y  +  [9.42391]  z  +  [9.42776]  =  0, 
y  +  [8.55847]  2.+  [9.03378]  =  0, 

2 -f  [8.58189a]  =  0. 


Value. 

Weight. 

Probable  Error. 

/  / 

-  0.0287 

4437 

/  f 

0.0062 

y  =  0.1095 

49 

0.0588 

^  =  -f-  0.0382 

(56 

0.050(5 

m  =  135,  y  =  S,  [rm  ■  3]  =  48.922,  r  =  0.4106. 
Probable  Values  of  R,  Z>,  o. 


(Quantity. 

Assumed  Value. 

Correction. 

Probable  Value. 

R 

/  f 

45.040(5 

0.0287 

1  1 

45.0119 

D 

2.1192 

—  0.1095 

2.0097 

0 

47.87 

+  0.04 

47.91 

Taking  1  "  of  latitude  =  101  ft./ the  difference  of  latitude  of 
the  two  observatories  is  75.3  ft.  =  0/^75. 

Adding  this  to  the  value  above,  the  result  is 

Latitude  of  the  Detroit  Observatory,  42^  16^  48.^416  ±  0. '4)51. 


V 


► 


CORHECTED  VALUES  OF  LATITUDE.  -  49 

Values  of  Latitude  Corrected  hy  Comimted  Probable  Values  of  P  and  D . 


No. 

Computed 

Value. 

1 

1 

Microra.  Cor. 

1 

Level.  Cor. 

1 

1 

^  a; 
a  ^ 

C.  ^ 

S-  > 

C 

Xo. 

• 

Computed  i 

Value. 

; 

1 

£ 

g 

O  1 

S 

1 

1 

Level  Cor.  ! 

i 

Corrected 

V  alue. 

1 

t  1 

44.53 

t  • 

-0.36 

!  / 

—0.34 

!  f 

43.83 

23 

t  f 

46.47 

/  f 

+0.26 

f  t 

+0.01 

t  t 

46.74 

o 

49.65 

_  22 

—  .17 

49.26 

24 

47.82 

+  .29 

.02 

1 

48.13 

i> 

O 

47.33 

+  .16 

-f  .02 

47.51 

25 

48.97 

—  .39 

+ 

.02 

48.60 

4 

48.75 

+  .08 

+  .14 

48.97 

26 

46.71 

+  .11 

+ 

.01 

46.83 

4 

47.31 

+  .26 

+  .02 

47.59* 

27 

48.20 

_  22 

+ 

.01 

47.99 

5 

48.13 

-f“  .  25 

V  .14 

48.52 

28 

46.20 

+  .17 

.00 

46.67 

() 

46.45 

f  .41 

+  .02 

46.88 

29 

52.95 

+  .23 

.00 

53.18 

7 

47.89 

--  .22 

—  .26 

47.41 

30 

49.21 

+  .53 

— • 

.05 

49.69 

8 

48.18 

+  .26 

+  .03 

48.47 

31 

46.54 

+  .26 

+ 

.04 

46.84 

9 

48.48 

+  .29 

+  .13 

48.90 

32 

47.20 

+  .26 

— 

.05 

47.41 

10 

47.93 

—  .39 

+  .04 

47.58 

33 

48.03 

+  .29 

.00 

48.32 

11 

46.60 

-f-  .03 

+  .02 

46.65 

34 

•46.61 

—  .39 

+ 

.05 

46.27 

12 

48.88 

+  .03 

.00 

48.91 

35 

47.61 

+  .11 

+ 

.02 

47.74 

13 

46.33 

-f  .29 

+  .01 

46.63 

36 

48.65 

-  .22 

+ 

.02 

48.45 

14 

49.41 

+  .11 

.00 

49.52 

37 

48.12 

+  .16 

— 

.25 

48.03 

15 

46.29 

-f  .01 

—  .01 

46.27 

38 

46.63 

+  .31 

— 

.20 

46.74 

16 

47.32 

+  .29 

—  .18 

47.43 

39 

47.43 

+  .26 

+ 

.02 

47.71 

17 

25.86 

+  .21 

4-  .04 

26.11 

40 

47.71 

+  .29 

— 

.01 

47.99 

18 

47.86 

+  .31 

+  .06 

48.23 

41 

49.36 

—  .39 

+ 

.01 

48.98 

19 

48.41 

—  .02 

+  .25 

48.64 

42 

47.75 

1+  .11 

.00 

47.86 

20 

47.02 

+  .26 

+  .02 

47.30 

43 

47.77 

—  .22 

1 

— 

.02 

47.53 

1 

21 

47.72 

—  .39 

+  .02 

47.35 

44 

47.76 

j+  .16 

— 

.01 

!  47.91 

1 

22 

47.84 

i 

:+  .11 

+  .03 

47.98 

45 

47.49 

!+  .31 

1 

— 

.18 

47.62 

*  Mean  48.28, 


c 


50  CORRECTED  VALUES  OF  LATITUDE. 

Vcdues  of  Latitude  Corrected  by  Computed  Probable  Values  of  11  and  7). 


Xo. 

^  .:3 

o  ^ 

Q 

Microm.  Cor. 

Level  Cor. 

1 

Corrected 

Value.  1 

1 

1 

No. 

Computed 

Value. 

i 

. 

0 

s— / 

r" 

P 

0 

0 

0 

'a! 

I 

Corrected 

Value. 

1 

46 

/  f 

48.79 

r  t 

-0.20 

/  • 

+  0.02 

/  / 

48.61 

69 

/  t 

6.21 

t  f 

-0.08 

/  / 

0.00 

f  ( 

6.13 

47 

46 . 58 

—  .25 

+• 

.02 

46.35 

70 

12.48 

+ 

.36 

.00 

12.84 

48 

47.36 

-  .22 

H- 

.04 

47.18 

71 

47.53 

— 

.20 

+  .02 

47.35 

49 

49.48 

+  .16 

.01 

49.63 

71 

47.29 

+ 

.07 

—  .02 

47.34* 

50 

48.80 

+  .35 

- 

.02 

49.13 

72 

46.30 

+ 

.11 

+  .05 

46. 4() 

51 

47.47 

-  .39 

+ 

.06 

47.14 

46.63 

+ 

.35 

-j.  .17 

47.15 

52 

48.25 

-  .22 

.20 

48.23 

1  74 

j 

46.94 

— 

.11 

-h  .25 

47.08 

53 

44.80 

H  .16 

+ 

.05 

44.01 

75 

48.21 

— 

.22 

+  .01 

48.00 

54 

46.03 

+  .31 

.01 

46.35 

76 

43.41 

+ 

.16 

+  .03 

43.60 

55 

46.99 

+  .35 

.02 

47.32 

i  77 

i 

48.77 

.07 

—  .08 

48.62 

56 

47.68 

+  .26 

+ 

.01 

47.95 

i  78 

47.64 

+ 

.26 

+  .08 

47.98 

57 

47.52 

+  .29 

— 

.04 

47.77 

79 

48.00 

'  - 

.10 

—  .05 

47.85 

58 

47.21 

-  .39 

.00 

46.82 

80 

49.07 

— 

.06 

.07 

48.94 

59 

47.38 

+  .11 

\ 

.02 

47.47 

1  81. 

49.42 

+ 

.01 

.05 

49.38 

60 

47.48 

+  .16 

+ 

.02 

47.66 

82 

47.88 

— 

.07 

+  .18 

47.99 

61 

47.24 

+  .31 

+ 

.04 

47.59 

1  83 

46.34 

— ■ 

.07 

—  .03 

46.24 

62 

47.48 

+  .35 

.00 

47.83 

i  84 

1 

12.04 

+ 

.36 

.00 

12.40 

63 

48.81 

—  .20 

+ 

.04 

48.65 

85 

1 

47.70 

— 

.10 

+  .03 

47.  ()3 

64 

48.02 

—  .22 

— 

.01 

47.79 

86 

47.63 

— 

.06 

.00 

47.57 

65 

47.30 

+  .26 

— 

.05 

47.51 

87 

46.27 

.23 

—  .05 

46.45 

()6 

49.31 

+  .35 

— 

.05 

49.61 

88 

49.01 

— 

.22 

+  .01 

48.80 

()7 

47.37 

-f  .35' 

.00 

47.72 

89 

48.46 

.16 

+  .05 

48.67 

()8 

45 . 57 

.06 

.00 

45.51 

90 

47.52 

— - 

.11 

+  .06 

!  47.47 

1 

*  Mean  47.34. 


I 

I 


COIUIECTED  VALUES  OF  LATITUDE.  51 

Vahies-qf  Latitude  Corrected  hy  Computed  Probable  Values  of  R  and  D. 


Xo. 

Computed 

Ynlue. 

1 

Microm.  Cor. 

i_  _ 

Level  Cor. 

! 

Corrected 

V^alue. 

Xo. 

Computed 

Value. 

Microm.  Cor. 

Level  Cor. 

Corrected 

Value. 

91 

/  / 

47.52 

/  r 

-0.09 

f  / 

f0.02 

/  t 

0 

47.45 

113 

r  / 

43.32 

/  f 

+0.23 

f  t 

+0.07 

/  ' 

43.62 

92 

50.90 

h 

.07 

f-  .05 

51.02 

114 

48.39 

+ 

.01 

+  .10 

48.50 

93 

47.29 

+ 

.23 

+  .01 

47.53 

115 

48.13 

+ 

.07 

—  .34 

47.86 

94 

47.48 

+ 

.02 

—  .01 

47.49 

116 

47.73 

— 

.07 

+  .18 

47.84 

95 

48.49 

— 

.22 

-f  .02 

48.29 

117 

48.39 

— 

.07 

+  .05 

48.37 

9() 

53.36 

+ 

.15 

-|-  .  04 

53.55 

•  118 

48.58 

+ 

.07 

—  .08 

48.57 

97 

47.44 

— 

.10 

f-  .01 

47.35 

119 

48.70 

— 

.20 

+  .01 

48.51 

98 

47.95 

— 

.09 

—  .29 

47.57 

120 

49.95 

+ 

.01 

.00 

49.96 

99 

48.81 

+ 

.07 

-|-  .  05 

48.93 

121 

47.81 

— 

.03 

—  .14' 

47.64 

100 

45.76 

+ 

.23 

—  .01 

45.98 

121 

48.02 

— 

.03 

—  .14 

47.85 

101 

48.98 

+ 

.11 

—  .22 

48.87 

121 

46.99 

— 

.08 

—  .18 

46.73* 

102 

46.82 

+ 

.02 

-  .04 

46.80 

122 

49.63 

— 

.07 

—  .01 

49.55 

103 

47.99 

+ 

.16 

+  .02 

48.17 

123 

48.76 

+ 

.07 

—  .01 

48.82 

104 

48.40 

+ 

.31 

-f-  .01 

48.72 

124 

48.37 

— 

.03 

—  .07 

48.27 

105 

48.60 

— 

.10 

-  .15 

48.35 

124 

47.93 

— 

.09 

—  .07 

47.77t 

100 

46.87 

— 

.07 

—  .04 

46.76 

125 

49.47 

+ 

.07 

—  .27 

49.27 

107 

47.26 

— 

.25 

+  .37 

47.38 

126 

45.67 

+ 

.11 

—  .16 

45 . 62 

107 

46.56 

.21 

+  .36 

46.71 

127 

45.27 

+ 

.02 

—  .09 

45.20 

108 

47.45 

+ 

.22 

+  .13 

47.80 

128 

47.50 

+ 

.07 

—  .21 

47.36 

109 

47.85 

+ 

.02 

—  .07 

47.80 

129 

47.69 

+ 

.02 

—  .01 

47 .  TO 

110 

46.86 

.31 

-h  .09 

47.26 

130 

48.30 

— 

.43 

+  .01 

47.88 

111 

48.39 

— 

.11 

+  .07 

48.35 

131 

47.68 

— 

.03 

+  .02 

47.67 

112 

48.25 

— 

.09 

+  .05 

48.21 

131 

47.65 

— 

.03 

+  .02 

47.64 

*Mean  47. 41  t  Mean  48.02. 


c 


52  CORKECTED  VALUES  OF  LATITUDE. 

Values  of  Latitude  Corrected  hy  Co  m'puted  Prohahle  Values  of  R  and  D. 


No. 

Computed 

Value. 

1 

Microm.  Cor. 

Level  Cor. 

Corrected 

Value. 

No. 

Computed 

Value. 

Microm,  Cor. 

1 

Level  Cor.  I 

i 

! 

Corrected 

Value. 

' 

131 

!  t 

47.24 

/  / 

—0.09 

/  t 

+0.02 

r  ! 

47.17* 

.3,3 

47.55 

t  • 

+0.20 

f  f 

—0.01 

t  r 

47.74 

132 

49.72 

—  .17 

+  .07 

49.62 

136 

48.36 

—  .03 

+  .03 

48.36 

133 

48.26 

—  .43 

+  .06 

47.89 

136 

48.37 

—  .03 

+  - 16 

48.50* 

134 

49.86 

—  .03 

—  .05 

49.78 

136 

48.26 

—  .09 

+  .08 

48.25t 

134 

49.13 

—  .03 

—  .05 

49.05 

137 

48.03 

-  .03 

—  .02 

47.98 

134 

48.38 

—  .09 

—  .17 

48.]2t 

138 

• 

46  ..82 

—  .21 

+  .02 

46.63 

*  Mean  47.49.  t  Mean  48.98,  i  .Mean  48.37. 


PK0IL4BLE  ERllOll  OF  OBSERVATION. 


53 


The  following  pairs,  with  the  corrected  latitudes  furnished  by 
them,  were  used  to  determine  the  probable  error  of  an  observa¬ 


tion.  The  result  is  0."539. 


Names.  No.  of  Obs. 

/  Cygiii  I  r, 

a  Cygni  . 

♦)TI.  Cepliei  I 

32VuJpeeulaf  | .  ‘ 

r  (\ygni  [  - 

^  ('ygni  I . 

Gr.  3415  ^  ^ 

A  Pegasi  .  ‘ 

20  Pegasi  )  i  ^ 

24(’ephei  ^ . 

31  Pegasi 

31  Cephei  ^ .  ‘ 

■  .  ( .  3 

4  (  assiopeijc  \ 

B.  A.  0.8195  ^ 

/  Anclromedfe  ^ . 


Names.  No.  of  obs. 

N 

}  Cephei  [ 

c^Piscium  C . 

a  Andromeda*  [ 

«  Cassiopeia*  ^ . 

B,  A,  C.79  [ 

-Andromeda  ^ . . 

e Andromeda  |  r- 

a  Cassiopeia  ^ .  ‘ 

B.  A.  C.  341  ^ 

38  Cassiopeia  ^ . 

(p  Persei  [  r- 

,3  Trianguli  . 

17  Tauri,  etc. 

9  H.  Camelopardalis  ^ .  (5 

(Mean  values) 


« 


VALUES  OF  LATITUDE  DEPENDING  ON  ZENITH- 
DISTANCE  OF  STARS  OBSERVED. 


In  forming  this  table  each  observation  received  the  same 
weight  as  the  corresponding  equation  of  condition;  and  the 
values  here  given  are  each  the  mean  by  weight  of  the  separate 
values  employed. 


Temp. 

0"  20° 

AVt. 

0 

1 

o 

o 

00°  -81° 

AVt. 

45  75" 

t  / 

47.88 

24 

t  r 

48.01 

10 

/  / 

47.07 

1 

30  45 

47.03 

13 

48.55 

8 

47.03  . 

1 

0  --  30 

48.37 

0 

1 

48.05 

2 

47.71 

1 

The  smaller  values  obtained  from  the  low  stars  seem  to  indi¬ 
cate  that  northern  stars  are  refracted  less  than  southern,  for 
the  same  zenith-distance;  and  that,  therefore,  the  layers  of  the 
atmosphere,  instead  of  being  parallel  to  the  surface  of  the  earth, 
are  depressed  more  rapidly  toward  the  north. 


THE  END. 


(54) 


